Estimation of the Mean Squared Error Sample Clauses

Estimation of the Mean Squared Error. In this Section we present a simulation experiment carried out to contrast the three alternative estimators of the Mean Squared Error of the NPEBLUP estimator θ˜E (ψˆ ) described in Section 6.2. Namely, the estimators we consider are the analytical estimator (6.11), the na¨ıve nonparametric bootstrap estimator msenaNPB (6.12) and the combined analytical and bootstrap estimator msebcNPB (6.13). The simulation study is carried out using real data coming from the Italian Agricultural Census of year 2000 for the Tuscany region, as in Molina et al. (2009), under two different settings. The small areas of interest are the 287 municipalities of the region, with Ni, i = 1,... , m, given by the census and the ni randomly generated from a Binomial distribution with parameters Ni and p = 0.05. These sampling data were used to compute, for each municipality i, the direct estimator of the mean agrarian surface area used for production of grape in hectares (θi) and its sampling variance (ψi). Information on the agrarian Table 6.2: Percentage Relative Root Mean Squared Error (RRMSE%) of the estimators of the small area means.
Sample 1
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